There are many ways to regularize the estimation of
the KR rearrangement.
For instance, one could
augment the average log-likelihood in
(REF ) with
a convex
penalty on the coefficients of
\(\widehat{S}\) —e.g., a ridge or lasso functional [1]}—yielding a
penalized maximum likelihood estimator.
In addition, one could constrain the function space for the estimator
by using only low-order nonlinear basis functions (see Appendix ).
In this section, we focus on the complementary idea of regularizing the estimation by imposing
sparsity constraints on \(\widehat{S}\) , i.e.,
by
dropping some variable dependence from each component
of the map, such that
\( \widehat{S}^k(z_1,\ldots ,z_k) =\widehat{S}^k(z_{j_1},\ldots , z_{j_p}, z_k)\) 
